AnarchyChess

Forcing stalemate if you're super down in material

Maybe if any promotion would lead to a stalemate

If your opponent plays strictly by a point system, like a computer might, and if the piece is threatened, it might be beneficial to keep the value low to trick the oppont to do something else, while you keep the useless pawn as an obstruction, which could somehow limit your opponent's future moves.

Anyway, it's apparantly not allowed.

Well exactly. I can't think of one. It could only be useful in a situation where having a dead weight in a cell would solve some problem or other, but I've no idea how.